Lectures 1 – Course OverviewLectures 1 – Course OverviewMonday January 7Monday January 7thth (start Ch. 1 on Wed. 9 (start Ch. 1 on Wed. 9thth))

•Organization of the course•Course web page•Breakdown of the grade•Schedule of topics and exams•Syllabus

•Overview of the course•History•Outline of topics

Reading: Reading: All of chapter 1 (pages 1 - 23)All of chapter 1 (pages 1 - 23)I will assign the 1I will assign the 1stst homework set on homework set on

Wed.Wed.

http://www.phys.ufl.edu/~hill/teaching/2008/4523/index.htmThe PHY4523 course web siteThe PHY4523 course web site

•All information is posted here•Syllabus, homework and exam policies, etc..•Homework assignments (incl. deadlines) and solutions •Course schedule with tentative exam dates•Solutions to exams and practice tests•A link to my PHY3513 course web page

•Weekly homework assignments: no excuse for NOT getting 80-100% on these. The deadlines vary from week to week. No late homework accepted.

•Homework assignments will be graded by a graduate TA. However, all questions about grading should be directed to the instructor (Hill).

•I will give short unannounced quizzes in roughly 30% of the lectures. We will use the SRS (HiTT). Remotes will be provided, but you are free to use your own also.

http://www.phys.ufl.edu/~hill/teaching/2005/3513/index.htmPHY4523 written examsPHY4523 written exams

In-class exams:In-class exams: there will be there will be threethree of these (in of these (in NPB 1002), each lasting 50 minutes, and starting NPB 1002), each lasting 50 minutes, and starting promptly at 11:45am. The tentative dates for these promptly at 11:45am. The tentative dates for these exams are: exams are:

Final:Final: There will be a cumulative 2 hour final exam There will be a cumulative 2 hour final exam (in NPB 1002) during finals week. (in NPB 1002) during finals week. You MUST take this You MUST take this exam.exam.

The best two scores out of the 3 in-class exams will be The best two scores out of the 3 in-class exams will be worth a total of 34% (17% each) towards your final grade. worth a total of 34% (17% each) towards your final grade. The final exam will be worth 34% towards your final The final exam will be worth 34% towards your final grade. grade.

You MUST take all 3 of these exams (see web site for You MUST take all 3 of these exams (see web site for policy on make up exams, or come and talk to policy on make up exams, or come and talk to instructor).instructor).

About the text bookAbout the text book

•If not available at the UF bookstore, try other bookstores around Gainesville.

•We will cover only the first 10 chapters.•If you still have the book by Ashley Carter, this can serve as an excellent supplementary text.

•This is the first time I have used the book by Bowley and Sanchez, so I cannot comment on accuracy of, e.g. solutions.

•Take some time to study the appendices at the end of the book. In particular, Appendices C to E will be essential for this course and homework problems may be assigned from this material. You will also find useful integrals in Appendix B.

•Homework assignments mainly from end of chapter problem sets. Numerical answers to ALL of the problems are given in Appendix G, including written solutions to the odd-numbered problems.

Introductory Statistical MechanicsIntroductory Statistical Mechanics, by R. Bowley and M. Sanchez, by R. Bowley and M. Sanchez

About the course and the instructorAbout the course and the instructor•In terms of the concepts, the pace should be comfortable. However, the level of mathematical sophistication is substantially higher than in PHY3513.

•There is plenty of time for class discussion. PLEASE DON’T BE SHY. Speak up!! Ask questions. This adds to the learning experience and to the overall enjoyment of the lectures. Don’t be afraid to ask me crazy questions. I am not afraid to admit that I do not know the answer.

•Lectures typically include: PowerPoint slides with important ideas (posted on-line); worked examples on the board (not posted on-line); some demonstrations; discussion; and quizzes.

•Feel free to come to my office (NPB2263) or lab (NPB B158) at any time to discuss anything related to the course. I will also make every effort to be in my office during office hours.

•I have some travel during this semester, and will arrange well qualified cover on these occasions.

http://www.phys.ufl.edu/~hill/teaching/2008/4523/index.htmPHY4523 gradingPHY4523 grading

• For those of you who have taken PHY3513 with me, note that these percentages are a bit different; there is slightly more emphasis on exams in this course.

• After the 2nd exam, I will be prepared to discuss your performance with you individually, and what grade(s) you may be tracking for.

• This is the first time that I have taught this course, so I cannot predict what score will correspond to what grade. However.......

An example of PHY4523 gradingAn example of PHY4523 gradingPHY 3513, 2006:PHY 3513, 2006:

15 15 AA (40%)(40%)8 8 B+B+ (22%)(22%)6 6 BB (16%)(16%)5 5 CC (14%)(14%)1 1 DD (3%)(3%)Note 83% A/B+/BNote 83% A/B+/B

PHY 3513, 2007:PHY 3513, 2007:11 11 AA (37%)(37%)6 6 B+B+ (20%)(20%)9 9 BB (30%)(30%)3 3 CC (10%)(10%)1 1 DD (3%)(3%)Note 87% A/B+/BNote 87% A/B+/B

PHY 3513 (Fall 2006)

50 55 60 65 70 75 80 85 90 95 1000

1

2

3

4 Mean 78%Median 81%

D

C+

BB+ A

Num

ber o

f stu

dent

s

Score (%)

DO THE HOMEWORK & COME TO DO THE HOMEWORK & COME TO CLASSCLASS

•IF YOU ARE HERE ONLY FOR THE GRADE, THE CHANCES ARE HIGH THAT YOU WILL DO POORLY.

20 30 40 50 60 70 80 90 100 11040

50

60

70

80

90

100

Ove

rall

Gra

de

Score on Homework

PHY 3513 (2005-2007)~100 data points

• Clear correlation Clear correlation between homework between homework and exam scores.and exam scores.

• Nevertheless, the Nevertheless, the exams require exams require understanding, i.e. understanding, i.e. you will not get away you will not get away with memorization of with memorization of homework problems. homework problems.

Statistical MechanicsAn Overview

The early history: thermodynamics and statistical physicsThe early history: thermodynamics and statistical physics

The early history: thermodynamics and statistical physicsThe early history: thermodynamics and statistical physics

*

The dawn of quantum mechanics and quantum statisticsThe dawn of quantum mechanics and quantum statistics

* Heike Kamerlingh Onnes became the 1st physicist to liquify helium.

The dawn of quantum mechanics and quantum statisticsThe dawn of quantum mechanics and quantum statistics

The dawn of quantum mechanics and quantum statisticsThe dawn of quantum mechanics and quantum statistics

Statistical MechanicsWhat will we cover?

A review of classical thermodynamics (1st 2 chapters)•Temperature, 1st law, functions of state, etc•Entropy and the 2nd law, irreversible processes

Probability and StatisticsProbability and Statistics

PHY 3513 (Fall 2006)

50 55 60 65 70 75 80 85 90 95 1000

1

2

3

4 Mean 78%Median 81%

D

C+

BB+ A

Num

ber o

f stu

dent

s

Score (%)

Probability and StatisticsProbability and Statistics

02468

1012141618

0 20 40 60 80 1000

Num

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f stu

dent

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Final score (%)

PHY2048 - Fall 2002458 studentsMean 63±0.5

Sigma 27.5±1.5Area 470±33

Probability and StatisticsProbability and Statistics

0 1 2 3 4 5 6 7 80

20

40

60

80

100

120

PHY2048 - Fall 2002 (test 2)

Mean 3.03±0.09Sigma 3.41±0.32Area 561±75

522 students

Num

ber o

f stu

dent

s

Score (out of 8)

Gaussian statistics: 2

2

1 exp22x x

f x

Probability and EntropyProbability and Entropy

Suppose you toss 4 coins. There are 16 (24) possible outcomes. Each one is equally probably, i.e. probability of each result is 1/16. Let W be the number of configurations, i.e. 16 in this case, then:

1 11 ; 1tot i

i

p P p W pW

Boltzmann’s hypothesis concerning entropy:

lnBS k Wwhere kB = 1.38 × 1023 J/K is Boltzmann’s constant.

The connection to thermodynamicsThe connection to thermodynamics

1/ 2

1/ 2

1/ 2

2

8

3

m

rms

kTvm

kTvm

kTvm

3/ 2

2 24 exp / 22mf v v mv kTkT

Maxwell-Boltzmann Maxwell-Boltzmann speedspeed distribution function distribution function

2 21 2 1 23 3 2 3

PV Nmv N mv N NkT

Equation of state:

The bridge to thermodynamics The bridge to thermodynamics through through ZZ exp / ;j

j

Z E kT js represent different configurations

1/ kT

Quantum statistics and identical Quantum statistics and identical particlesparticlesIndistinguishable events

Heisenberguncertaintyprinciple

The indistinguishability of identical particles has a profound effect on statistics. Furthermore, there are two fundamentally different types of particle in nature: bosons and fermions. The statistical rules for each type of particle differ!

ApplicationsApplications

Insulating solid Diatomic molecular gas

Specific heats:

Fermi and Bose gases